Programming Contest

Review for Exam 1

Fall 2004

You may have one sheet of notes

Chapters from Carrano/Savitch

• Chapters 17 Dictionaries

• Chapter 18 Dictionary Implementation

• Chapter 19 Hashing

• Chapter 24 Trees

• Chapter 25 Tree implementations

• Chapter 26 A BST Implementation

• Chap 27 A Heap Implementation

Lecture Topics

• Major categories

– Java programming

– Dictionaries

– Hashing

– Trees

– Heaps

Lab topics

• Use the Sorted Dictionary class

• Create a simple hash table

• Use the HashMap class

• Tree Concepts

• Implement a thesaurus using hashing

• Vary the hash function & collision resolution

• Build a BST

Java review

• Mostly done looking at the Dictionary class

– Java file I/O

– Java interfaces

• Comparable interface

• Iterator interface

– Difference between interfaces & abstract classes

– Interfaces

– StringTokenizer

– Iterators

– Writing generic code

Dictionary ADT

• A dictionary uses a key to retrieve information that is related to the key

• The dictionary can be implemented several ways

– Sorted array

– Sorted linked list

– Hash table

– Binary search tree

• We looked at two Dictionary classes that implemented a dictionary interface

– One objective in doing that was to review different Java constructs

– The other was to become familiar with the Dictionary ADT

Hashing

• General idea of hashing

• Hash functions

• Time complexity of perfect hashing

• Collision resolution methods

• Load factor

Hash functions

• Criteria for good hash functions

– Quick and easy to compute

– Minimize the number of collisions

– Achieve an even distribution of the records across the range of indices (uniform hashing function)

• Writing a hash function

– First, convert the key to an integer

• Many ways to do this

• Using a polynomial hash code for strings seems to work well

– Use Horner’s method to evaluate the polynomial

– Then, compress to size of the array

Collision resolution methods

• Open address

– Advantages & disadvantages

– Types

• Linear probing

• Quadric probing

• Double hashing

• Separate chaining

– Advantages & disadvantages

• I may ask you about what you did for your hashing lab, and the results.

Load factor

• Optimal depends on the type of collision resolution

• Open addressing should be about 0.5

• Separate chaining can go as high as 1 or 2 without much degradation

– Books seem to recommend .75

Rehashing

• If the load factor gets too high, the table should be rehashed

• This involves

– Doubling the table size

– Sending all the keys through the new hash function

Trees

• Definitions of leaf, path, height, parent, child

• Full m-ary trees

– Definition?

– Theorems about relationships between

m: # children,

i: # interior nodes

n: # total nodes

L: # leaves

Tree traversal & recursion

• Inorder

– Recursively visit all nodes in the left subtree

– Process the root node

– Recursively visit all nodes in the right subtree

• Preorder

– Process the node, go left, then go right

• Postorder

– go left, then go right, then rocess the node,

Binary Trees

• Every node has at most two children

• Types of binary trees

– Expression trees

– Binary Search Trees

– Heaps

• As long as the tree stays balanced, the height of the tree is the log of the number of (nodes +1)

• If you have a full binary tree with 127 nodes, what is its height?

– Log 128 = 7; 2⁷=128

Binary Search Trees

• Ordering

• Know how these operations work and the time complexity (but do not feel you must be able to reproduce the code)

– Adding

– Deleting

– Searching

Heaps

• Heap order property

• Heap structure property

• How heaps are stored in the machine

• Adding an element to a heap

• Deleting the max or min element from a heap

• Time complexity of the major operations of a heap